Actually if you have a roll cage, then you can experience multiple impacts (e.g. you can hit the cage a number of times should you happen to roll) and even in autox you are required to have an SA helmet ... so watch out for that. Also with a full-race car and road racing/hill climb/rally you are required to have nomex underwear, socks, suit and the nomex-lined helmet for fire protection as Stuart mentioned.
A motorcycle helmet is designed for one BIG impact ... think about hitting a curb when sliding along a road after crashing , hi-siding etc.
For autox, we do not experience as high a speed as at a track and no fender-to-fender paint swapping so it is reasonable to accept a "lower" standard. Usually motorcycle helmets are cheaper ... although I'm noticing lately that there does not seem to be as much difference for the Snell-rated motorcycle helmets.
Also for autox you can have an open helmet unless you have a car with no windshield and requires that you have eye-protection (kind of obvious, eh?) ... e.g. proper googles or a full-faced helmet.
Just watch out for DOT helmets that are NOT Snell-rated. (I find that a bit of weird one because most of the time it is just that the manufacturer just did not pay the extra fees to pay for the Snell testing and hence the Snell rating ... Often they do not make any change to the helmet ... but whatever ... ).
Who'd 'a thunk that helmet issues could be so complex, eh?
R